Bloch-McConnell equation

Hansen " now present an evaluation of the approximate solutions of the Bloch-McConnell equations of a chemically exchanging system. The evaluation... 

The n-site Bloch-McConnell equations describe the evolution of nuclear spin magnetization in the laboratory or rotating frames of reference for molecules subject to chemical or conformational interconversions between n species with distinct NMR chemical shifts. Trott and Palmer used perturbation theory to approximate the largest eigenvalue of the Bloch-McConnell equations and obtain analytical expressions for the rotating-frame relaxation rate constant and for the laboratory frame resonance frequency and transverse relaxation rate constant. The perturbation treatment is valid whenever the population of one site is dominant. The new results are generally applicable to investigations of kinetic processes by NMR spectroscopy. 

Devaux et al. have described in some detail the use of the Bloch equations to relate electron spin-spin interactions between spin-labeled lipids to diffusion constants. This method was originally employed by Trauble and Sackmann,50 Scandella et al.,42 Devaux and McConnell,10 and Devaux et al.11 to measure diffusion constants in multibilayer model membranes and in biological membranes. In all cases diffusion constants of the order of those reported previously were obtained. 

In a simple transfer process of nucleus X between Larmor frequencies of two sites A and B the Bloch equations have been modified by McConnell... 

Returning now to a discussion of the Redfield equations (40) we first note that, with our choice in (39), the only nondiagonal elements that are coupled to each other are p,2 and P34. Except for the driving-field terms these equations therefore have a form very similar to the modified Bloch equations postulated by McConnell. The quantum-mechanical derivation of (40), however, leads to new insight and restrictions in the use of these equations in the optical domain (Section IV). 

For the intermediate exchange where the resonances change upon passing from a slow into a fast regime, the lineshape can be described by McConnell s modification of the Bloch equations [17], For a first-order two-site exchange without homonuclear scalar coupling, for example, the lineshape is given by ... 

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